Question

Simplify 16/3(6/8b+9/2). Write in simplest form.

Answer 1

3/8 = 0.37500
hope its right...!!!!!

Answer 2

 16/3(6/8b+9/2) Final result : 4 • (b + 6)

Step by step solution :Step  1  : 9 Simplify — 2 Equation at the end of step  1  : 16 6 9 —— • ((— • b) + —) 3 8 2Step  2  : 3 Simplify — 4 Equation at the end of step  2  : 16 3 9 —— • ((— • b) + —) 3 4 2 Step  3  :Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple 

      The left denominator is :       4 

      The right denominator is :       2 

        Number of times each prime factor
        appears in the factorization of: Prime 
 Factor  Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 {Left,Right} 2212 Product of all 
 Prime Factors 424

      Least Common Multiple: 
      4 

Calculating Multipliers :

 3.2    Calculate multipliers for the two fractions 


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well. 

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respectiveMultiplier.

L. Mult. • L. Num. 3b —————————————————— = —— L.C.M 4 R. Mult. • R. Num. 9 • 2 —————————————————— = ————— L.C.M 4 Adding fractions that have a common denominator :

 3.4       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3b + 9 • 2 3b + 18 —————————— = ——————— 4 4 Equation at the end of step  3  : 16 (3b + 18) —— • ————————— 3 4 Step  4  : 16 Simplify —— 3 Equation at the end of step  4  : 16 (3b + 18) —— • ————————— 3 4 Step  5  :Step  6  :Pulling out like terms :

 6.1     Pull out like factors :

   3b + 18  =   3 • (b + 6) 

Final result : 4 • (b + 6)